The field of the disclosure relates generally to digital transmission systems, and more particularly, to multi-carrier wired, wireless, and optical digital transmission systems.
Conventional digital transmission systems typically include both linear and non-linear distortion. However, for the purposes of the following discussion, use of the term “distortion” is generally intended to refer to linear distortion only. Conventional digital transmission systems also utilize symbols with coefficients, either in the time domain (TD) or frequency domain (FD), which are generally complex-value sequences. That is, the coefficients of the complex symbols typically include both a real component and an imaginary component, or alternatively, a magnitude and a phase value. Time and frequency domains are related, and the two domains are duals of each other. That is, for a plot or a sequence of numerical values, it must be known whether to observe the plotted numbers as time domain or frequency domain values.
This distinction is of particular significance when considering multi-carrier (MC) digital transmissions, such as with orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) transmissions. OFDM symbols, for example, when plotted, appear as discrete values in the frequency domain, but look like random noise in the time domain. In contrast, if a transmission is single carrier (SC), its symbols can be viewed as discrete values in the time domain, but look like random noise in the frequency domain. Thus, multi-carrier and single carrier transmissions are viewed in different domains.
One type of distortion that is known to severely affect digital transmissions is multipath. Multipath linear distortion is sometimes referred to as “echoes,” “ghosts,” or “dispersion.” An example of an echo distortion is shown in FIG. 1A. FIG. 1A is a schematic illustration depicting a conventional transmission system 100. System 100 includes a transmitter 102 with a transmitting antenna 104 and a receiver 106 with a receiving antenna 108. Transmitter 102 modulates a baseband signal onto a carrier, thereby forming an RF signal 110 for communication over a signal path 112 between transmitter 102 and receiver 106. Data over signal path 112 includes telephony, computer code, file data, network data, internet, world wide web (WWW), entertainment video, video phone, security alarm signals, etc. The data may be widely broadcast, or intended for only the single receiver 106. Signal path 112 includes (i) a direct path portion 114, and (ii) an echo path portion 116 that reflects off of a reflecting object 118. Data traveling over direct path portion 114 results in a direct signal portion 120 at receiver 106, and data traveling over echo path portion 116 results in an echo signal portion 122 at receiver 106. Direct signal portion 120 and echo signal portion are collectively received by receiver 106 as a received signal 124.
Thus, the presence of echoes from reflections (e.g., from reflecting object 118) causes received signal 124 to be distorted by the presence of echo signal portion 122 combined with a direct signal portion 120. In some cases, direct path portion 114 may be blocked by an obstruction 126 between transmitter 102 and receiver 106, and the only signal reception possible will be from echo signal portion 122 over echo path portion 116. In many cases, the received signal includes multiple echo signals. If the frequency response of the signal path 112 is measured, the presence of a strong echo will cause ripples in the magnitude of the response, where the reciprocal of the frequency difference between peaks is the time delay of the echo from path 116, relative to the direct signal 120.
On wired signal paths, echoes may alternatively occur from impedance mismatches within coaxial networks. With multipath linear distortion, one or more copies of the original signal—typically with a delay and attenuation—are added to the original signal. On wireless signal paths, the multipath linear distortion, and therefore the attenuated and delayed copies, may be caused by signals reflecting from structures, such as buildings, water towers, etc. In the example of radiated transmissions such as received broadcast analog television pictures, the multipath linear distortion may appear as additional fainter images superimposed on the intended image, along with a typical delay relative to the intended image received over a direct transmission path.
On single mode fiber optic cable using coherent optical signals, the transmission characteristics are different relative to RF (sub-100 GHz) wired and wireless signal paths. For example, a 1550 nm wavelength laser has an optical frequency of 193e12 Hz. In single mode glass fiber, an impairment called Chromatic Dispersion (CD) is encountered, which is similar to group delay encountered, typically from filters, at much lower wired and wireless frequencies. Signals at different frequencies (optical wavelengths) travel at different speeds down the fiber optic cable and this linear distortion needs to be equalized to minimize inter-symbol interference (ISI). This impairment becomes more severe with increasing bandwidth and more severe with longer fiber optic cable spans. This type of signal interference is different from echoes, which are not typically encountered on fiber optic transport media. Coaxial cables and free space, on the other hand, experience virtually no group delay (chromatic dispersion). Thus, CD is created by different wavelengths of a signal traveling at different speeds, whereas echoes are reflected copies of the same signal.
On optical fiber, different polarizations can be used for simultaneous transmission of two different signals, but because fiber cores sometimes have elliptical shapes, as opposed to round shapes, signals with different polarizations travel at different rates, resulting in an impairment that must be removed at the receiver. Satellites and microwave towers also use vertical and horizontal polarizations for signals propagating in free space, but free space propagation does not experience polarization distortions. In some conventional OFDMA and single-carrier frequency-division multiple-access (SC-FDMA) systems, overlapping signals from multiple transmitters are combined from multiple transmitters at RF frequencies. At optical frequencies, however, these overlapping signal techniques experienced optical beat interference (OBI) problem unless the optical signal phase purity is high. Therefore, echo problems are generally encountered on wired and wireless channels, but not on fiber optic cable (e.g., due to use of angled connectors).
In the case of digital transmissions, mild multipath distortion will increase the bit error rate (BER) in the presence of random noise or other additive impairments, and may thus be corrected, whereas un-equalized severe multipath distortion, on the other hand, may render the received data useless for further processing at the receiver end. Other types of linear distortions, such as a non-flat frequency response or a group delay, may also affect or impair digital transmissions. These types of distortions may result from imperfect filters and/or amplifier tilt.
Some conventional techniques have been utilized to eliminate, or at least equalize, multipath linear distortion in the time domain or frequency domain. One conventional time domain technique utilizes an adaptive equalizer to correct for multipath distortion. The adaptive equalizer sums a received distorted signal with a delayed version of the distorted signal, in order to cancel the received echoes. This cancellation process is referred to as equalization, or “de-ghosting.” Conventional adaptive equalization schemes sometimes employ a filter architecture such as a finite impulse response (FIR) filter, which utilizes a number of taps (either hardware or software) that are configured to execute a multiply-accumulate operation, and programs coefficients in the adaptive equalizer to cancel received echoes. Such programming may utilize a particular reference signal, also referred to as a training signal or “ghost-canceling” signal, so that the programmed coefficients are computed as an inverse of the channel response. The frequency and the impulse response of the channel may also be determined as intermediate steps, and, in the time domain, tap coefficients are computed as the reciprocal of the impulse response. In some instances, the adaptive equalizer is programmed using blind equalization techniques. An exemplary FIR filter architecture is disclosed in U.S. Pat. No. 5,886,749, which is incorporated by reference herein.
Echoes on cable lines can come in two varieties: single recursion and multiple (infinite) recursion. An infinite recursion occurs, for example, by an echo tunnel as a signal bounces back and forth in the tunnel, getting weaker on each pass. FIG. 1B is a graphical illustration depicting examples of conventional time domain plots 128 for a multiple recursion 130 and a single recursion 132 on an echo signal path, and respective adaptive equalizer solutions (impulse response) 134 implemented to correct the encountered recursion 130 or 132. As shown in illustration 128, the adaptive equalizer solution 134M that corrects multiple recursion echo 130 though, is itself a single recursion. In contrast, where the main signal path experiences single recursion 132 (e.g., as can happen with two signal paths), the adaptive equalizer solution 134S that corrects single recursion echo 132 though, is a multiple recursion. In the conventional systems, multiple recursion solution 134M requires more taps, or more time, than would single recursion solution 134S to remove an echo. If the echo is stronger, even more taps, with significant energy, are required.
Conventional adaptive equalization techniques, however, are significantly limited with respect to complex signals that require processing of a large number of coefficients (e.g., greater than 8 or 64). Because the FIR filter utilizes linear convolution, the rate of required computations increases as the product of the number of taps, multiplied by the clocking speed of the taps. For hardware-implemented taps, a large number of coefficients will significantly increase the cost and size of the physical structure that performs the adaptive equalization. For software-implemented taps, an exponential increase will significantly increase the required processing speed of the programming that performs computations. Large quantities of taps are particularly necessary where, for example, the clock frequency of the equalizer is high, and where a received echo is long.
Some conventional techniques attempt to solve the multiple-computational problems associated with adaptive equalization by taking a received distorted signal in the time domain, separating the time domain signal into blocks, and then transforming the blocks into the frequency domain, such as through use of a fast Fourier transform (FFT). The transformed blocks thus become sets of frequency domain subcarriers, and each frequency domain subcarrier may then be multiplied by a single complex coefficient to remove the associated linear distortion. This process is known as frequency domain equalization (FDE).
Once the linear distortion is removed, the frequency domain blocks are converted back into time domain blocks. A problem occurs, however, if the blocks are contaminated with foreign or extraneous energy, such as might occur from echo energy transporting distortion from a previous block. Conventional systems address this energy transportation problem through use of cyclic prefixes (CP), which are a set of time domain symbols copied from the end of the block and pasted onto the front of the block.
FIG. 2A is a graphical illustration of a time domain signal 200 of a conventional OFDM transmission 202 having a cyclic prefix 204, utilized in accordance with transmission system 100, FIG. 1A. Typically, an OFDM carrier signal is the sum of one or more OFDM symbols, each symbol made up of a plurality of orthogonal subcarriers, and with baseband data on each subcarrier being independently modulated. In an embodiment, OFDM transmission 202 is a carrier signal transmitted using technology such as the Data Over Cable Service Interface Specification (DOCSIS), version 3.1, or one or more of many known and burgeoning wireless standards. As described above, OFDM implements a plurality of different subcarriers, all of which are harmonics of a fundamental, to obtain orthogonality.
DOCSIS specifications conventionally utilize OFDM for downstream signals and OFDMA for upstream signals. OFDM and OFDMA are complimentary. OFDM is typically used in the downstream transmission where there is one transmitter (e.g., a Cable Modem Termination System (CMTS)) sending information to multiple receivers (e.g., cable modems). OFDMA is typically used in the upstream transmission where there are multiple transmitters (e.g., the cable modems) transmitting to one receiver (e.g., the CMTS). The cyclic prefix is therefore commonly used in both OFDM and OFDMA.
The cyclic prefix functions as a “guard time” that separates data bursts, and allows any micro-reflection from one burst to die out before the next burst is received, thereby eliminating interference from one block to the next. The cyclic prefix is therefore considered particularly essential over an HFC network, where reflections frequently occur. Reflections are often created by impedance mismatches on the HFC network and result from a number of issues, including manufacturing tolerances of passive hardware such as taps, power inserters, and splitter, active hardware such as amplifiers, and connectors. Combined multiple micro-reflections therefore, create linear distortions, which cause a number of impairments to signal transmission, including amplitude ripple (standing waves), group delay ripple, inter-symbol interference, and degraded modulation error ratio (MER) on digital signals transmitted on the HFC network. For a conventional multicarrier equalization processes, the cyclic prefix should be longer than any echo in the signal path. Accordingly, various durations of cyclic prefixes are utilized to accommodate a variety of echo delays in the HFC network, thereby significantly increasing the overhead of the network, but without carrying any useful customer information in the transmission of the cyclic prefix.
OFDM transmission 202 includes, for example, first harmonic subcarrier 206, second harmonic subcarrier 208, third harmonic subcarrier 210, and fourth harmonic subcarrier 212. For ease of explanation, only four such subcarriers of OFDM transmission 202 are illustrated, but typically, many more subcarriers exist. Each of the harmonically-related subcarriers 206, 208, 210, 212 may have different magnitude and phase values. When all four subcarriers 206, 208, 210, 212 are combined, or summed, for transmission, the summed result is a single composite signal 214.
Orthogonality allows each of the original subcarriers to be separated at the receiver (e.g., receiver 106, FIG. 1), such as with utilization of Fourier processes. That is, a discrete Fourier transform (e.g., an FFT) converts a set of time domain values into frequency domain values, and an inverse discrete Fourier transform (e.g., an IFFT) converts frequency domain values into time domain values. The larger the transform, the greater is the efficiency improvement by using an FFT, as opposed to a simple discrete Fourier transform. The FFT block sizes may be efficiently implemented with a block size of radix 2 (2{circumflex over ( )}n, where n is an integer), such as 256, or 1024, but other efficient transform block sizes are possible. Cyclic prefix 204 is created by copying symbols from an end region 216 (shown shaded in gray) of composite signal 214, and pasting the copied signals onto the beginning region thereof as a guard interval. Cyclic prefix 204 thus allows circular convolution or FDE to be performed on OFDM transmission 202, without suffering interference from a previous OFDM block if there is an echo on the channel. However, for this example, it is assumed that the echo is shorter than cyclic prefix 204.
FIG. 2B is a graphical illustration of a frequency domain signal 218 of OFDM transmission 202, FIG. 2A. That is, frequency domain signal 218 represents a spectral plot of OFDM transmission 202 in the frequency domain. Frequency domain signal 218 may be obtained by performing a discrete Fourier transform or an FFT on composite time domain signal 214, FIG. 2A. As illustrated in FIG. 2B, each of time domain harmonic subcarriers 206, 208, 210, 212 has a respective frequency domain component subcarrier 220, 222, 224, 226, each having both a magnitude and a phase value. Under these conventional techniques, OFDM transmissions may be viewed in either the time domain or the frequency domain. However, composite signal 214 appears noise-like, or random in the time domain, which is problematic for multiple-carrier symbols. In comparison, some single-carrier symbols, such as single-carrier frequency-division multiple-access (SC-FDMA) can also be viewed either in the time domain or the frequency domain, but such single-carrier symbols resemble noise when viewed in the frequency domain. Accordingly, it is desirable to develop systems and methods capable of receiving, equalizing, and utilizing the same multiple-carrier or multiple-access symbols in both the time domain and the frequency domain.
Cyclic prefixes provide block-to-block isolation, and thus transmission of digital information is often performed with blocks of data. Some conventional systems use linear code, such as a Reed-Solomon code or Low-Density Parity Check (LDPC) codes, for purposes of forward error correction (FEC), which allows a percentage of erred symbols to be corrected by the code. Use of cyclic prefixes, however, requires additional resources to transmit the extra data that constitutes the cyclic prefix. The required cyclic prefix data reduces the bandwidth efficiency of transmissions, thereby limiting the amount of data that can be transmitted within a given frequency band, while also requiring additional power and decreasing the battery life of system components. Moreover, as described above, cyclic prefixes are not completely effective in the case where the cyclic prefix portion of time domain data is shorter than the length, or duration, of a received echo.